Summary
We study the Schrödinger Hamiltonian corresponding to a finite number of δ’-interactions supported by concentric spheres. In particular we discuss the self-adjointness of the Hamiltonian, derive the resolvent equation and study the spectral properties.
Riassunto
Si studia l’hamiltoniana di Schrödinger che corrisponde a un numero fïnito di interazioni δ’ sostenute da sfere concentriche. In particolare si discute la capacità dell’Hamiltoniana di essere autoaggiunta, si deriva l’equazione risolutiva e si studiano le proprietà spettrali.
Резюме
Мы исследуем Гамильт ониан Шредингера, соответствующий конечному числу σ′-вз аимодействий, опираю щихся на концентрические сфе ры. В частности, мы обсужда ем самосопряженный Гамильтониан, выводи м уравнение резольвенты и исслед уем спектральные сво йства.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Albeverio, F. Gesztesy, R. Høegh-Krohn andH. Holden:Solvable Models in Quantum Mechanics. Texts and Monographs in Physics (Springer Verlag, Berlin, 1988).
J.-P. Antoine, F. Gesztesy andJ. Shabani:J. Phys. A,20, 3687 (1987).
F. Gesztesy, H. Holden andW. Kirsch:On energy gaps in a new type of analytically solvable model in Quantum Mechanics, preprint LPTHE (Orsay, France, 1986).
R. A. Adams:Sobolev Spaces (Academic Press, New York, N.Y., 1975).
M. Abramowitz andI. A. Stegun:Handbook of Mathematical Functions (Dover Publications Inc., New York, N.Y., 1972).
N. I. Akhiezer andI. M. Glazman:Theory of Linear Operators in Hilbert Space, Vol.2 (Pitman Publishing Inc., Boston, London, Melbourne, 1981).
L. Dabrowski andJ. Shabani:Singular interactions with support on surfaces and curves, preprint in preparation.
N. Dunford andJ. T. Schwartz:Linear Operators. Part II:Spectral Theory (Interscience Publishers, New York, N.Y., London, 1963).
M. Reed andB. Simon:Methods of Modern Mathematical Physics, Vol. 4:Analysis of Operators (Academic Press, New York, N. Y., San Francisco, Cal., London, 1978).
J. Weidmann:Linear Operators in Hilbert Space (Springer Verlag, Berlin, 1980).
J. Shabani:J. Math. Phys. (N. Y.),29, 660 (1988).
Author information
Authors and Affiliations
Additional information
On leave of absence from Département de Mathématiques, Université du Burundi, BP 2700 Bujumbura, Burundi.
Rights and permissions
About this article
Cite this article
Shabani, J. Some properties of the Hamiltonian describing a finite number of δ’-interactions with support on concentric spheres. Nuov Cim B 101, 429–437 (1988). https://doi.org/10.1007/BF02828921
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02828921